Academic Year 2018-2019
Advanced Fluid Mechanics
Transition to turbulence & turbulence - Applications to thermoconvection, aerodynamics & wind energy
This module was set up by Emmanuel Plaut (EP) and Joachim Peinke. However, this year, a colleague of J. Peinke, Michael Hölling (MH), from the university of Oldenburg, gave the part focussed on Turbulence & wind energy.
Find here the latest version of our lecture notes.
Hereafter we give the planning and a few information.
In sessions 1 to 6, with EP, the students will use Mathematica; in sessions 7 to 9, with MH, the students will use R.
Find here a collection of texts of past exams, with elements of solution.
Nous remercions la Fondation Mines Nancy et le programme Erasmus+ pour leur soutien, qui nous permet d'inviter MH à donner 3 sessions dans ce module, ainsi qu'une conférence générale.
Natural thermoconvection, Rayleigh - Bénard thermoconvection: linear stability analysis with slip boundary conditions
[ essential of the video presentation, slightly reworked ; movie gallery of DNSs of thermoconvection flows of F. X. Trias ]
Personal homework 1 due by January 14 (EP)
At the very beginning of session 2 on Monday,
January 14, give me
an hand-written personal solution of exercise 1.1.
Scoring scale:
Q. 1: 4 P ; Q. 2: 6 P ; 1 P of bonus if you use good english.
Vous avez le droit de rédiger en français...
Session 2 January 14 (EP)
Rayleigh - Bénard thermoconvection with slip boundary conditions: linear and weakly nonlinear stability analysis
[ essential of the video presentation ]
Session 3 January 16 (EP)
Rayleigh - Bénard thermoconvection: weakly nonlinear analysis, supercritical bifurcation, elements on further transitions and on the case of no-slip boundary conditions; Lorenz model & chaos; confined geometry - flow reversals...
Preparatory work: finish ex. 1.4 at home !
Nota bene: bring your laptop with Mathematica, we will perform some formal computations to solve, e.g., ex. 1.5 !
[ essential of the video presentation ; chaos in the Lorenz system (on YouTube !) ]
Transition in open shear flows: generalities, the case of plane Poiseuille flow
Nota bene: bring your laptop with Mathematica, we will perform computations to solve pb. 2.1 !
[ essential of the video presentation ]
Session 5 January 30 (EP)
Transition in plane Poiseuille flow: linear and weakly nonlinear stability analysis, Tollmienn - Schlichting waves
Preparatory work : (re)write a Mathematica program that solves problem 2.1 up to the question 5.
[ essential of the video presentation ]
Homework 2 due by February 4 (EP)
Form 5 groups of 2 students that will work together (but not with the other groups !). Each group will write a structured and commented Mathematica notebook (or package) to solve exercise 2.2 Linear stability analysis of PPF at high Reynolds number. I should be able to run this program by myself and get all the results. One of the 2 students of each group should upload the program on the ARCHE page of the module before Monday February 4 9:00 in the morning. I created a section for this purpose on this ARCHE page.
Session 6 February 4 (EP)
Transition in plane Poiseuille flow: weakly nonlinear stability analysis, subcritical bifurcation to Tollmienn - Schlichting waves, subcritical & saddle-node bifurcations. Transition in open shear flows...
Nota bene: bring your laptop with Mathematica, we will perform some computations !
[ essential of the video presentation ]
Session 7 February 5 (MH)
Wind energy : conversion principles - Rotor blade aerodynamics
Nota bene: bring your laptop with R, we will perform some computations !
[ essential of the video presentation (through ARCHE) ]
Session 8 February 6 (MH)
Rotor blade aerodynamics - Stochastic (Langevin) power curve
[ essential of the video presentation (through ARCHE) ]
Session 9 February 7 (MH)
Wind field and Turbulence
[ essential of the video presentation (through ARCHE) ]
Wind Energy and the Need to Understand Turbulence
The only documents allowed were the printed versions of
the lecture notes
(chapter 1; chapters 2 and 3).
The focus was on chapter 1 and on the beginning of chapter 3
(sections 3.1 to 3.2).
It was asked to bring your scientific pocket calculator and
your laptop,
to perform small numerical calculations and
computations
with Mathematica.
See the page collection.htm !..
Emmanuel Plaut |
Last modified: Tue Feb 12 17:21:55 CET 2019 |